(2653490 - 1)2 - 2
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help)value
Description:(2653490 - 1)2 - 2
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p393 : Rodenkirch, Cksieve, OpenPFGW
Decimal Digits:393441   (log10 is 393440.18373291)
Rank (*):5675 (digit rank is 1)
Entrance Rank (*):3733
Currently on list? (*):no
Submitted:6/14/2016 16:13:56 CDT
Last modified:6/14/2016 22:20:40 CDT
Removed (*):1/6/2018 14:41:01 CDT
Database id:121779
Status Flags:TrialDiv
Score (*):43.7687 (normalized score 0.9054)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
fieldvalue
prime_id121779
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(2^653490-1)^2-2" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing (2^653490-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.01% proof)


(2^653490-1)^2-2 is prime! (21154.5439s+0.0074s)
[Elapsed time: 5.88 hours]
modified2017-01-27 05:57:11
created2016-06-14 16:23:01
id167418

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.